Two towns, P and Q, are 15 cm apart on a map with a scale of 1:200,000. A road linking P to Q has a circuity ratio of 1.4. What is the actual length of the road?

First, convert map distance to actual straight-line distance: 15 cm × 200,000 = 3,000,000 cm = 30 km. The circuity ratio (route length ÷ straight-line distance) is 1.4, so the actual road length = 30 km × 1.4 = 42 km. A common error is forgetting to apply the circuity ratio, giving 30 km, or applying it to the map distance before converting.